Both organisations were criticised by local MSP Claire Baker after the Macmillan Crossroads service, which offers respite to those caring for relatives struck down by cancer, was forced to close through lack of funding.
The MSP wrote to the co
uncil and NHS Fife to ask why they didn't step in to ensure the service could continue.
"There is no one else offering this service in Fife," she said.
"Macmillan Crossroads service has been a vital support for families in Fife, providing respite to carers of terminally ill cancer patients at what are unimaginably difficult times for people.
"Following the closure of this service, many families in Fife will now have to do without much-needed help.
"Furthermore, the Macmillan staff that have spent years building experience will now be lost to the profession."
The service officially closed last week after seven years of providing palliative care for patients.
But the council and the local NHS team say they have funded the service this year and neither had received a new funding request from Macmillan.
A spokesman for NHS Fife said it had supported Crossroads across Fife with funding of £122,577 this year, plus a one-off contribution of £22,979 to extend the service by six months, to give it time to find new funding.
"The NHS has received central resources to support the delivery of the Carer Information Strategy over the next three years," said the spokesman.
"Crossroads did not submit a bid for funding but we would be happy to consider future bids for funding to support the strategy for 2009-10 or 2010-11."
Similarly, the council said it had provided £110,000 in funding to the service this year and has also recently committed to creating a specialist post to provide social work services to people suffering from cancer, as well as their carers and families.
Kenny Leinster, a senior manager of the council's social work services department, said: "We have not had a request for additional funding from Crossroads.
"We will consider a request from them alongside any other grant applications.
"The social work service is in discussion with the NHS and Cancer Network Fife to create a Fife-wide strategy for cancer."
